Session__5_notes

# Session__5_notes - Probability of Z>1.55(area in tail 0.45...

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0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 1.55 Probability of Z>1.55 (area in tail)

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0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 1.55 P=.0606 Probability of Z>1.55 (area in tail)
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 1.55 P=1-.0606=.9394 Probability of Z<1.55

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0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 -1.55 1.55 P=.0606+.0606 P=.1212 Probability of Z<-1.55 and Z>+1.55 (area in both tails)
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 1.55 P=.5-.0606=.4394 Probability of Z>0 and Z<1.55

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Note: You can work backwards to find a Z- score that corresponds with a given proportion. Example 1: What is the Z-score that has 25% of the area above it in the normal distribution?
Example 2: What is the Z-score that has 85% of the area above it in the normal distribution?

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Review: Z-scores can be put onto other standardized scales. Example: T-score (μ=50, σ=10) T i = 50 + 10 z i T-scores are often provided on psychological tests to communicate with other professionals or clients. They help communication with others as there are no negative numbers. The client needs to be informed that anything about 50 is above average. Anything below 50 is below average.
What you should know from last week’s class: 1. Definition of kurtosis 2. Definition and how to interpret a Z-score 3. Change raw scores to Z-scores 4. Change Z-scores to raw scores 5. Using Z-scores to compare raw scores from different distributions 6. Determine the area above/below a point on the normal distribution (one-tailed) 7. Determine the area between two points on the normal distribution (two-tailed) 8. How to convert a Z-score to other standardized scale (i.e. T-score)

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Imagine that our class is a population. We want to know about the average IQ score. If we repeatedly draw samples from a population, we can construct a frequency distribution of the sample statistics. The differences between the sample means is due to chance (sampling error). Graphic from www.gseis.ucla.edu/courses/ed230a2/notes/t1.html .
The frequency distribution of statistics (sample means) is also called a sampling distribution. Note: We are not talking about distributions of scores anymore. We are talking about the distribution of sample means. The sampling distribution contains the sample means for all the possible random samples of a particular size that can be obtained from a population.

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all possible random samples in a population, the mean of the sampling distribution will equal μ. Because of this feature, we consider x-bar to be an unbiased estimate of μ. The
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Session__5_notes - Probability of Z>1.55(area in tail 0.45...

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